Joseph Krasil'shchik's introductory lectures on the Geometry of Differential Equations

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Autumn 2010

Lectures take place at the Independent University of Moscow on Wednesday evenings from 17:30 to 19:10 in room 206

The first lecture is on 15 September

Short syllabus

Jets of bundles
The Cartan distribution
Symmetries of the Cartan distribution
The Lie-Bäcklund theorem

Nonlinear differential equations and operators
Classical symmetries of differential equations, their computation and application
The Bianci-Lie theorem

Infinite jets and geometric structures on them
The Cartan distribution on infinite jets and its symmetries
Linearizations and evolutionary vector fields

Prolongations of differential equations
Infinitely prolonged equations
Higher symmetries of differential equations, their computation and application
Recursion operators for symmetries

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